Fresnel lens and liquid crystal display device

ABSTRACT

A display device including liquid crystal display panels, arrays of convergently transmissive elements for forming an erect and real image, and fresnel lenses for magnifying the image. The configured surface of the fresnel lens is arranged on the light incident side. The configured surface includes periodic ridges with flat crests and inclined surfaces. Shading layers are provided on the flat crests to eliminate ghosts.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a fresnel lens having a shading layerand a display device such as a liquid crystal display device includingmagnifying fresnel lenses.

2. Description of the Related Art

Liquid crystal display devices can have relatively thin structures andhave been used for many applications. Recently, projection type liquidcrystal display devices having larger screens have been developed. Atypical projection type liquid crystal display device includes aprojection lens which projects a magnified image onto a screen. Also,optical elements other than a projection lens can be used for magnifyingan image.

For example, Japanese Unexamined Patent Publication (Kokai) No. 5-188340discloses a projection type liquid crystal display device includingliquid crystal display panels, fresnel lenses for magnifying imagesproduced by liquid crystal display panels, and a screen. In this case,the liquid crystal display device also includes arrays of convergentlytransmissive elements, and a screen. Each of the arrays of convergentlytransmissive elements is adapted to form an erect and real image havingan identical size to an object, and each of the fresnel lenses serves tomagnify the image from the array of convergently transmissive elements.

The convergently transmissive elements are made from plastic or glass inthe form of transparent rods having the diameter of 1 mm to 2 mm, sothat refractive index changes in each of the transparent rods in theradial direction thereof. By appropriately selecting the length and thedistribution of refractive index thereof, it is possible to use each ofthe convergently transmissive elements so that it can form an erect andreal image having an identical size to an object. A plurality ofconvergently transmissive elements are arranged in a close relationshipto each other with the end surfaces of the elements arranged in a lineor in a plane, to thereby form a row or an array of convergentlytransmissive elements. The array of convergently transmissive elementscan be used as an imaging device for producing an erect and real imagehaving an identical size to an object. The imaging device using thearray of convergently transmissive elements has advantages, comparedwith a usual spherical lens, in that a focal distance is very short andan optical performance is uniform in the line or plane so that anadjustment of the distance between the lenses is not necessary.

However, when the array of convergently transmissive elements is used asthe imaging device, it is not possible to change a magnification of theimage although it is possible for individual convergently transmissiveelements to be changed in magnification by changing the length of theelements. This is because magnified images produced by the individualconvergently transmissive elements are inconsistently superposed, one onanother, in the array and a normal image cannot be formed. Therefore,the array of convergently transmissive elements can be used only as afull size imaging device, and it is necessary to provide a magnifyingmeans in addition to the array of convergently transmissive elements.

Japanese Examined Patent publications (Kokoku) No. 58-33526 and No.61-12249 disclose an imaging device including an array of convergentlytransmissive elements and a convex lens or a concave lens as amagnifying means which is arranged on the inlet side or on the outletside of the array of convergently transmissive elements. The convex lensor the concave lens can be of a single lens or a composite lens of aplurality of lens components to realize a desired magnification.However, when this imaging device is used with a magnifying device in aLiquid crystal display device, a problem arises in that resolving powerof the lens changes from the central portion to the peripheral region.

It has been found that a good image is obtained if the resolving powerMTF is greater than 50 percent under the condition of 4 (1 p/mm) i.e., 4pairs of white and black spots per millimeter. However, it is generallydifficult to establish an image having, resolving power MTF greater than50 percent in the above described prior art. It is necessary that lightpasses through the peripheral region of the liquid crystal display panelat an angle of approximately 10 degrees relative to the normal line ofthe liquid crystal display panel in order to ensure resolving power MTFgreater than 50 percent. The smaller the angle at the peripheral regionis, the smaller the magnification of the device is. As a result, it isnot possible to realize a liquid crystal display device having a thinstructure if a convex lens or a concave lens is used with an array ofconvergently transmissive elements, although the array of convergentlytransmissive elements by itself can provide a liquid crystal displaydevice having a thin structure.

Accordingly, a magnifying element is desired which can be used with anarray of convergently transmissive elements and which can realize aliquid crystal display device having a thin structure. The use of afresnel lens with an array of convergently transmissive elements isdisclosed in the above described Japanese Unexamined Patent Publication(Kokai) No. 5-188340, but the manner in which the fresnel lens is usedis not described in this prior art. The inventors have recently foundthat a good result is obtained if a fresnel lens is used as a magnifyingelement.

Further, in a liquid crystal display device, there is a problem thatbrightness of an image on a peripheral region of the screen is reducedrelative to the brightness of the image on the central region of thescreen.

SUMMARY OF THE INVENTION

The object of the present invention is to provide a fresnel lensconstructed such that light is made incident to a configured surfacethereof.

Another object of the present invention is to provide a display devicehaving a thin structure by appropriately arranging a fresnel lens.

Another object of the present invention is to provide a display devicein which the brightness of a screen is improved.

According to one aspect of the present invention, there is provided afresnel lens comprising a body having a flat surface and a configuredsurface with periodic ridges, each of the ridges including a flat crestextending generally parallel to the flat surface and at least oneinclined surface extending from the flat crest toward the flat surface,and a shading layer provided on the fiat crest of each of the ridges.

Preferably, the flat crests have varying widths depending on thepositions of the ridges. In this case, the at least one inclined surfacecomprises a main inclined surface arranged on one side of the flat crestand designed such that light is mainly incident to the body from themain inclined surface and a minor inclined surface arranged on the otherside of the flat crest from the main inclined surface.

Preferably, the width of the flat crest is determined by the followingrelationship: ##EQU1## where d is the width of the flat crest, p is thepitch of the ridges, r is the angle of a major light ray made incidentto the body from the main inclined surface relative to the axis, θ₁ isthe angle the main inclined surface relative to the flat surface, and θ₂is the angle of the minor inclined surface relative to the axis.

According to a further aspect of the present invention, there isprovided a display device comprising at least one image modulator, anarray of convergently transmissive elements receiving light from said atleast one image modulator for forming an erect and real image, a fresnellens including a body having a flat surface and a configured surfacewith periodic ridges, the fresnel lens being arranged so that light ismade incident from the array of convergently transmissive elements tothe configured surface of the fresnel lens, and a screen receiving lightfrom said at least one image modulator via the array of convergentlytransmissive elements and the fresnel lens.

Preferably, each of the ridges includes a flat crest extending generallyparallel to the flat surface and at least one inclined surface extendingfrom the flat crest toward the flat surface, and a shading layer isprovided on the flat crest of each of the ridges.

Preferably, the flat crests have varying widths depending on thepositions of the ridges. Preferably, the at least one inclined surfacecomprises a main inclined surface arranged on one side of the flat crestand designed such that light is mainly incident to the body from themain inclined surface and a minor inclined surface arranged on the otherside of the flat crest from the main inclined surface.

Preferably, the at least one image modulator comprises a plurality ofliquid crystal display panels, and the array of convergentlytransmissive elements and the fresnel lens are arranged for every liquidcrystal display panel. Preferably, four sets of the liquid crystaldisplay panels, the arrays of convergently transmissive elements and thefresnel lenses are arranged, with each set arranged in respectivequarter portions in a rectangular region, the screen having a totaldisplay area four times greater than a display area necessary to receivean image from one set of the liquid crystal display panel, the array ofconvergently transmissive elements and the fresnel lens.

Preferably, a partition is arranged on or near the screen between twoadjacent sets of the liquid crystal display panels, the arrays ofconvergently transmissive elements and the fresnel lenses for preventinglight from straying from one set into the adjacent set.

Preferably, the screen has a predetermined display area, and said atleast one image modulator has a main display area and a peripheralcompensating area arranged such that the main display area forms animage on the predetermined display area via the array of convergentlytransmissive elements and the fresnel lens and the peripheralcompensating area forms an image just outside the predetermined displayarea via the array of convergently transmissive elements and the fresnellens. Preferably, the peripheral compensating area of said at least oneimage modulator is controlled to provide an image which is generallyidentical to a portion of an image delivered from the main display areaof the at least one image modulator near the peripheral compensatingarea.

Preferably, between two adjacent liquid crystal display panels, saidperipheral compensating area of one liquid crystal display panel iscontrolled to provide an image which is generally identical to a portionof an image delivered from the main display area of the adjacent liquidcrystal display panel near the peripheral compensating area of said oneliquid crystal display panel.

According to a further aspect of the present invention, there isProvided a display device comprising at least one image modulator,optical lens for magnifying an image output by said at least one imagemodulator, a screen for receiving an image from said at least one imagemodulator via said optical lens, the screen having a predetermineddisplay area, and said at least one image modulator has a main displayarea and a peripheral compensating area arranged such that the maindisplay area forms an image on the predetermined display area via saidoptical lens and the peripheral compensating area forms an image justoutside the predetermined display area via said optical lens.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will become more apparent from the followingdescription of the preferred embodiments, with reference to theaccompanying drawings in which:

FIG. 1 is a cross-sectional view of a liquid crystal display deviceaccording to the embodiment of the present invention;

FIG. 2 is a plan view illustrating the arrangement of four liquidcrystal display panels of FIG. 1;

FIGS. 3A to 3C are views illustrating the feature of one of theconvergently transmissive elements of FIG. 1;

FIG. 4 is a view illustrating the propagation of light in theconvergently transmissive element;

FIG. 5 is a view illustrating formation of an erect and real imagehaving an identical size to an object;

FIG. 6 is a diagrammatic perspective view of an array of convergentlytransmissive elements of FIG. 1;

FIG. 7 is a view illustrating the imaging surface and how the resolvingpower is reduced;

FIG. 8 is a cross-sectional view of the fresnel lens of FIG. 1;

FIG. 9 is a partial plan view of the fresnel lens of FIG. 8;

FIG. 10 is a cross-sectional view of a portion of the fresnel lens ofFIGS. 8 and 9;

FIG. 11 is a cross-sectional view of a conventional fresnel lens;

FIG. 12 is similar to FIG. 10, but includes several dimensionalcharacters for calculating the width of the shading layer on the flatcrest of the ridge of the configured surface of the fresnel lens;

FIG. 13 is a plan view of the modified liquid crystal display panels;

FIG. 14 is a view illustrating the pictures produced by the main displayarea and the peripheral compensating area of the liquid crystal displaypanel;

FIG. 15 is a view illustrating the image on the screen produced by twoadjacent liquid crystal display panels;

FIG. 16 is a view illustrating the pictures produced by the main displayarea and the image of the peripheral compensating area of the liquidcrystal display panel of FIG. 15;

FIG. 17 is a diagrammatic cross-sectional view of a liquid crystaldisplay device similar to the arrangement of FIG. 13;

FIG. 18 is a cross-sectional view illustrating the course of lightemerging from the main display area and the peripheral compensating areato the screen;

FIG. 19 is a plan view illustrating an element of an image on a screen;

FIG. 20 is a plan view of several elements of an image on a screen; and

FIG. 21 is a view illustrating how the brightness of the image at theperipheral region of the screen is reduced.

DESCRIPTION OF THE PREFERRED EMBODIMENT

FIGS. 1 and 2 show the liquid crystal display device 10 according to thepresent invention. The liquid crystal display device 10 includes fourliquid crystal display panels 12 which are arranged in respectivequarter portions in a rectangular region. Each liquid crystal displaypanel 12 includes an effective display region 12a and a non-displayregion 12b around the effective display region 12a, the non-displayregion 12b being necessary for attaching a drive circuit or the like tothe panel for driving the liquid crystal in the panel. Therefore, animage is not formed on the non-display region 12b and a discontinuousimage is formed if four liquid crystal display panels 12 are directlyseen. The embodiment realizes a continuous multi-display fromdiscontinuous images from four liquid crystal display panels 12, byproviding a magnifying element.

In FIG. 1, the liquid crystal display device 10 includes a backlight 14on the rear side of the panels 12, and arrays 16 of convergentlytransmissive elements on the front side of the respective panels 12. Thearea of each of the arrays 16 of convergently transmissive elements islarger than the area of the effective display region 12a, but smallerthan the total area of the panel 12 including the non-display region12b. Each array 16 of convergently transmissive elements can form anerect and real image having an identical size to an object, i.e., animage produced by the liquid crystal display panel 12.

The liquid crystal display device 10 includes fresnel lenses 18 on theoutput side of the arrays 16 of convergently transmissive elements,respectively. Each fresnel lens 18 includes a transparent body having aflat surface 18a and a configured surface 18b, in a saw-shape incross-section, with concentrically periodic ridges 19, as shown in FIGS.8 and 9. In the present invention, the fresnel lens 18 is arranged suchthat light is mainly incident onto the configured surface 18b of thefresnel lens 18. In the arrangement of FIG. 1, the configured surface18b faces the array 16. The flat surface 18a is thus arranged on thelight emerging side.

The liquid crystal display device 10 also includes a screen 22 having ascreen fresnel lens 20 on the front side of the fresnel lenses 18. Lightbeams emerging from the fresnel lenses 18 divergently travel toward thescreen 22 so that light beams emerging from the adjacent fresnel lenses18 meet on the screen 22 without a discontinuity. Therefore, thenon-display regions 12b of the liquid crystal display panels 12 cannotbe seen by a person watching the screen 22. The liquid crystal displaypanels 12 are one example of an image modulating means, and other typesof image modulating means, which merge light, can be used.

The array 16 comprises a plurality of convergently transmissive elements16a and the features of one of the convergently transmissive elements16a is shown in FIGS. 3A to 3C. The convergently transmissive element16a is made from plastic or glass in the form of transparent rod havingthe diameter of 1 mm to 2 mm. The refractive index of the element 16achanges in the body thereof in the radial direction, as shown in FIG.3C. The distribution of refractive index n(r) is represented by thefollowing quadratic function

    n(r)=n.sub.0 (1-g.sup.2 r.sup.2 /2)

where r is the distance from the vertical axis, n_(O) is refractiveindex on the vertical axis, and g is a distribution constant of therefractive index.

Light enters the convergently transmissive element 16a from its endsurface and is bent toward a portion thereof at which refractive indexis higher while light passes through the convergently transmissiveelement 16a, so that light travels along a periodically snaked course,as shown in FIG. 4. The cycle P is expressed by P=2π/g. If the length Zof the convergently transmissive element 16a is selected from therelationship of P/2<Z<3P/4, an erect and real image having an identicalsize to an object can be formed, as shown in FIG. 5. The distance L isthe distance between the object and the image.

FIG. 6 shows that the convergently transmissive elements 16a arearranged in a close relationship to each other with the end surfacesthereof arranged in a line or in a plane, to thereby form the array 16.An erect and real image having an identical size to an object can beformed by the array 16. The imaging device using the array 16 ofconvergently transmissive elements 16a offers advantages in that a focaldistance is very short, and the optical performance is uniform in theline or plane. However, it is not possible for the array 16 ofconvergently transmissive elements 16a to change the magnification ofthe image relative to an object, although it is possible for individualconvergently transmissive elements 16a to change the magnification ifthe length of the elements 16 is changed. This is because magnifiedimages formed by the individual convergently transmissive elements 16aare inconsistently superposed one on another in the array 16 and anormal image is not formed in the array 16. Therefore, the array 16 ofconvergently transmissive elements 16a can be used only as a full sizeimaging device, and the fresnel lenses 18 are used as a magnifyingmeans.

In the embodiment, the area of the effective region 12a of the liquidcrystal display panel 12 is 211.2 mm×158.4 mm, and the requiredmagnification (a value of the sum of the area of the effective region12a and the area of the ineffective region 12 divided by the area of theeffective region 12a) is 1.09. Regarding the convergently transmissiveelements 16a, the refractive index n is 1.507, the distribution constantof refractive index g is 0.1847, the length Z is 18.89 mm, and thediameter is 1.18 mm. The magnifying fresnel lens 18 is made from acrylhaving refractive index of 1.494 and has a radius of curvature in whichthe central curvature (cuy) is -0.00813668, the secondary constant is-0.775202×10⁻⁸, the tertiary constant is 0.318549×10⁻¹³, the quarticconstant is -0.720974×10⁻¹⁹, and the quintic constant is-0.717576×10⁻²⁵. The angle (AEP) of light emerging from the outermostperipheral position of the fresnel lens 18 relative to the normal lineof the fresnel lens 18 is 28.3 degrees. The screen fresnel lens 20serves to convert light beams emerging from the magnifying fresnel lens18 with a variety of angles into parallel light beams, and is made fromMS having refractive index of 1.537. The resolving power MTF in thisexample is shown in the following table.

    ______________________________________                                                      MTF (%)                                                         AEP (°)                                                                              2 (1 p/mm)                                                                              4 (1 p/mm)                                            ______________________________________                                        28.3          89.7      64.0                                                  ______________________________________                                    

In the further embodiment, the shape of the configured surface 18b ofthe fresnel lens 18 is changed so that the angle (AEP) of light emergingfrom the outermost peripheral position of the fresnel lens 18 ischanged. The resolving power MTF is examined while changing the angle(AEP). In this example, the refractive index n of the convergentlytransmissive elements 16a is 1.505, the distribution constant of therefractive index g is 0.1847, the length Z is 18.895 mm, and thedistance L is 20 mm. The thickness of the fresnel lens 18 is 2 mm andrefractive index is 1.494. The fresnel lens 18 is arranged to contactthe array 16 of convergently transmissive elements 16a. In thisarrangement, the curvature of the fresnel lens 18 is set in a parabolicshape so that a light beam (referred to as the main light beam) parallelto the optical axis of the fresnel lens 18 emerges from the outermostperipheral position of the fresnel lens 18 at an angle (AEP), and thefocal point is at a position on a line passing through the center of thefresnel lens 18. The resolving power MTF in this example is shown in thefollowing table. It should be noted that the configured surface 18b ison the light incident side and the flat surface 18a is on the lightemerging side.

    ______________________________________                                                      MTF (%)                                                         AEP (°)                                                                              2 (1 p/mm)                                                                              4 (1 p/mm)                                            ______________________________________                                        10            99.7      98.9                                                  20            98.1      92.7                                                  30            88.7      61.1                                                  40            88.9      61.5                                                  ______________________________________                                    

As will be understood from this table, the obtained values for MTF aresatisfactory even at an angle (AEP) of 40 degrees. Note that this resultis obtained in an arrangement where the configured surface 18b is on thelight incident side and the flat surface 18a is on the light emergingside.

It can be said that an image is formed substantially in a plane,however, the imaging surface is somewhat curved. Therefore, if the focalpoint is at a position on a line passing through the center of thefresnel lens 18, a value for MTF at a peripheral position may bereduced. In the above table, the values for MTF at the angles (AEP) of10 to 30 degrees are obtained when the focal point is at a position on aline passing through the center of the fresnel lens 18, but the valuefor MTF at the angle (AEP) of 40 degrees is obtained when the focalpoint is adjusted so that a value for MTF at the center of the fresnellens 18 is identical to a value for MTF at the outermost peripheralposition of the fresnel lens 18.

The following table shows the result of a test regarding resolving powerMTF obtained when the flat surface 18a is on the light incident side andthe configured surface 18b is on the light emerging side and the otherconditions are similar to those of the above example. This result shouldbe compared with resolving force MTF obtained when the configuredsurface 18b is on the light incident side and the flat surface 18a is onthe light emerging side.

    ______________________________________                                                      MTF (%)                                                         AEP (°)                                                                              2 (1 p/mm)                                                                              4 (1 p/mm)                                            ______________________________________                                        10            95.8      84.0                                                  12            90.8      65.0                                                  13            86.9      55.4                                                  14            81.6      41.5                                                  15            76.1      28.8                                                  20            26.6      5.5                                                   ______________________________________                                    

According to an estimation by observing the screen, it has been foundthat a produced image is good when a value for MTF is greater than 50percent under the condition of 4 (1 p/mm). Therefore, in thiscomparative test, it can be said that an angle (AEP) equal to or lowerthan 13 degrees is satisfactory but the curvature of the fresnel lens islimited to this extent.

The inventors further tried to analyze the reason why the resolvingpower MTF is reduced when the flat surface 18a is on the light incidentside and the configured surface 18b is on the light emerging side.

As shown in FIG. 7, it has been found that the focal length of thefresnel lens 18 becomes shorter as the position is displaced from thecenter of the fresnel lens 18 to the periphery thereof, and an imagingsurface is distorted relative to the screen 22 as shown by the brokenline F. In FIG. 7, the array 16 of the convergently transmissiveelements 16a and the fresnel lens 18 are shown, but the fresnel lens 18is arranged such that the configured surface 18b is on the lightemerging side.

In the analysis of the distorted imaging surface, the angle (AIM)between light beams 30 and 31 which are inclined to the main light beamon either side of the main light beam at identical angles relative tothe main light beam is noted. The angle (AIM) between light beams 30 and31 becomes smaller when light is made incident to the fresnel lens 18,and the angle (AIM) becomes greater when light emerges from the fresnellens 18, regardless of which surface is on the light incident side. Thistendency is stronger as the angle between the incident or merging lightand the incident or emerging surface becomes greater, that is, thistendency is stronger with respect to the configured surface 18b.Therefore, the angle (AIM) between light beams 30 and 31 becomes greaterin the arrangement where light emerges from the configured surface 18b,and an image is formed far from the screen 22 as the angle (AIM) becomesgreater, with the result that resolving power MTF is reduced. The angle(AIM) does not become so greater in the arrangement where light emergesfrom the flat surface 18a, and in this case, it is possible to form animage on the screen 22.

FIG. 10 shows the details of the fresnel lens 18 of FIG. 1. As describedabove, the fresnel lens 18 has the flat surface 18a and the configuredsurface 18b with concentrically periodic ridges 19. Each of the ridges19 includes a flat; crest 19a extending generally parallel to the flatsurface 18a and an inclined surface 19b extending from the flat crest19a toward the flat surface 18a. A minor surface 19c which isperpendicular to the flat surface 18a in FIG. 10 is arranged on theopposite side of the flat crest 19a from the inclined surface 19b. Ashading layer 19d is provided on the flat crest 19a of each of theridges 19. The shading layer 19d can be easily formed by printing sincethe flat crest 19a is parallel to the flat surface 18a.

FIG. 11 shows a conventional fresnel lens 18 having ridges 19. It willbe understood that the flat crest 19a of FIG. 10 is formed by cuttingthe apex of the ridge 19 of FIG. 10. In the conventional fresnel lens 18shown in FIG. 10, there is a problem of a straying beam inducing aghost. That is, if light S is made incident to the inclined surface 19bat a position near the surface 19c, light S is reflected by the minorsurface 19c and changes its course in an uncontrolled direction tothereby induce a ghost. The shading layer 19d is provided to solve thisproblem.

As will be understood from FIG. 8, the shape or the slope of the ridges19 changes depending on the positions of the ridges 19, and it ispreferable that the flat crests 19d have varying widths depending on thepositions of the ridges 19.

As shown in FIG. 12, the surface 19c may be inclined relative to theflat surface 18a for the reason of fabrication of the fresnel lens 18.As will be apparent, the main inclined surface 19b arranged on one sideof the flat crest 19a is designed such that light is mainly incident tothe body of the fresnel lens 18 from the main inclined surface 19b, andthe minor inclined surface 19c is arranged on the other side of the flatcrest 19a from the main inclined surface 19b.

Preferably, the width of the flat crest 19a is determined by thefollowing relationship: ##EQU2## where d is the width of the flat crest19a, p is the pitch of the ridges 19, r is the angle of a major lightray made incident to the body from the main inclined surface 19arelative to the axis, θ₁ is the angle the main inclined surface 19brelative to the flat surface 18a, and θ₂ is the angle of the minorinclined surface 19c relative to the axis of the fresnel lens 18.

FIGS. 13, 17 and 18 show the modified liquid crystal display device 10,which includes four sets of the liquid crystal display panels 12, thearrays 16 of convergently transmissive elements 16a and the fresnellenses 18, and a screen 22. The four sets are arranged in respectivequarter portions in a rectangular region. The screen 22 has a totaldisplay area four times greater than a predetermined display area 22pnecessary to receive an image from one set of the liquid crystal displaypanel 12, the array 16 of convergently transmissive elements and thefresnel lens 18. That is, the screen 22 has a predetermined display area22p for each of the liquid crystal display panel 12.

A partition 26 is arranged on or near the screen 22 between two adjacentsets of the liquid crystal display panels 12, the arrays 16 ofconvergently transmissive elements and the fresnel lenses 18 forpreventing light from straying from one set into the adjacent set.

Each liquid crystal display panel 12 includes an effective displayregion 12a and a non-display region 12b around the effective displayregion 12a, as described with reference to FIG. 2. The effective displayregion 12a is further divided into a main display area 12x and aperipheral compensating area 12y. The main display area 12x forms animage on the predetermined display area 22p via the array 16 ofconvergently transmissive elements and the fresnel lens 18. Theperipheral compensating area 12y forms an image just outside thepredetermined display area 22p via the array 16 of convergentlytransmissive elements and the fresnel lens 18. That is, the peripheralcompensating area 12y does not contribute to the formation of the actualimage on the screen 22, but compensates for a loss in brightness in theperipheral region of the liquid crystal display panel 12. As an example,the effective display region 12a includes 640×480 pixels, and the maindisplay area 12x includes 620×465 pixels.

As shown in FIG. 14, the peripheral compensating area 12y of the liquidcrystal display panel 12 is controlled to provide an image I₁ which isgenerally identical to a portion I₁ of an image delivered from the maindisplay area 12x of the liquid crystal display panel 12 near theperipheral compensating area 12y.

As alternatively shown in FIGS. 15 and 16, the peripheral compensatingarea 12y of the liquid crystal display panel 12 is controlled to providean image I₂ which is generally identical to a portion I₂ of an imagedelivered from the main display area 12x of the adjacent liquid crystaldisplay panel 12 near the peripheral compensating area 12y of said oneliquid crystal display panel 12.

FIG. 19 shows an element 50 of an image on a screen 22. The element 50should be a point at which several light beams are focussed, but infact, light beams may scatter to a certain region 51 due to anaberration of the magnifying fresnel lens 18. Therefore, brightness ofthe element 50 may be reduced. FIG. 20 shows several elements 50, 50a,50b, 50c, and 50d, with their scattering regions 51, 51a, 51b, 51c, and51d. The element 50 receives light from the other elements 50a, 50b,50c, and 50d and brightness of the element 50 may be compensated to someextent. FIG. 21 shows a peripheral portion of the screen 22 when theperipheral compensating area 12y is not provided. There are severalelements 50, 50a, 50b, 50c, and 50d, with their scattering regions 51,51a, 51b, 51c, and 51d on the peripheral portion of the screen 22, butbrightness of these elements may not be compensated since there are notsurplus light components outside the predetermined display area 22p.

As shown in FIG. 18, the peripheral compensating area 12y produces lightoutside the predetermined display area 22p and does not contribute tothe formation of an actual image, but light emerged from the peripheralcompensating area 12y may include scattered light components whichcompensate for the reduced brightness on the peripheral portion of thescreen 22.

We claim:
 1. A fresnel lens comprising a body having a flat surface anda configured surface with periodic ridges;each of the ridges including aflat crest extending generally parallel to the flat surface and at leastone inclined surface extending from the flat crest toward the flatsurface, wherein the flat crests have varying widths depending on thepositions of the ridges; and a shading layer provided on the flat crestof each of the layers.
 2. A fresnel lens according to claim 1, whereinthe at least one inclined surface comprises a main inclined surfacearranged on one side of the flat crest and a minor inclined surfacearranged on the other side of the flat crest from the main inclinedsurface.
 3. A fresnel lens according to claim 2, wherein the width ofthe flat crest is determined by the following relationship: ##EQU3##where d is the width of the flat crest, p is the pitch of the ridges, ris the angle of a major light ray made incident to the body from themain inclined surface relative to the axis, θ₁ is the angle the maininclined surface relative to the flat surface, and θ₂ is the angle ofthe minor inclined surface relative to the axis.
 4. A display devicecomprising:at least one image modulator; an array of convergentlytransmissive elements receiving light from said at least one imagemodulator for forming an erect and real image; a fresnel lens includinga body having a flat surface and a configured surface with periodicridges, the fresnel lens being arranged so that light is made incidentfrom the array of convergently transmissive elements to the configuredsurface of the fresnel lens; a screen receiving light from said at leastone image modulator via the array of convergently transmissive elementsand the fresnel lens; and wherein an angle (AEP) of light emerging froman outermost portion of the fresnel lens relative to a line normal tothe fresnel lens is in a range of between approximately 13 and 40degrees.
 5. A display device according to claim 4, wherein each of theridges includes a flat crest extending generally parallel to the flatsurface and at least one inclined surface extending from the flat cresttoward the flat surface, and a shading layer is provided on the flatcrest of each of the ridges.
 6. A display device according to claim 5,wherein the flat crests have varying widths depending on the positionsof the ridges.
 7. A display device according to claim 6, wherein the atleast one inclined surface comprises a main inclined surface arranged onone side of the flat crest and designed such that light is mainlyincident to the body from the main inclined surface, and a minorinclined surface arranged on the other side of the flat crest from themain inclined surface.
 8. A display device according to claim 7, whereinthe width of the flat crest is determined by the following relationship:##EQU4## where d is the width of the flat crest, p is the pitch of theridges, r is the angle of a major light ray made incident to the bodyfrom the main inclined surface relative to the axis, θ₁ is the angle ofthe main inclined surface relative to the flat surface, and θ₂ is theangle of the minor inclined surface relative to the axis.
 9. A displaydevice according to claim 4, wherein said at least one image modulatorcomprises a plurality of liquid crystal display panels, and the array ofconvergently transmissive elements and the fresnel lens are arranged forevery liquid crystal display panel.
 10. A display device according toclaim 9, wherein four sets of the liquid crystal display panels, thearrays of convergently transmissive elements and the fresnel lenses arearranged, with each set arranged in respective quarter portions in arectangular region, the screen having a total display area four timesgreater than the display area necessary to receive an image from one setof the liquid crystal display panel, the array of convergentlytransmissive elements and the fresnel lens.
 11. A display deviceaccording to claim 10, wherein a partition is arranged on or near thescreen between two adjacent sets of the liquid crystal display panels,the arrays of convergently transmissive elements and the fresnel lenses;whereby the partition prevents light from straying from one set into anadjacent set.
 12. A display device according to claim 4, wherein thescreen has a predetermined display area, and said at least one imagemodulator has a main display area and a peripheral compensating areaarranged such that the main display area forms an image on thepredetermined display area via the array of convergently transmissiveelements and the fresnel lens and the peripheral compensating area formsan image just outside the predetermined display area via the array ofconvergently transmissive elements and the fresnel lens.
 13. A displaydevice according to claim 12, wherein said peripheral compensating areaof said at least one image modulator is controlled to provide an imagewhich is generally identical to a portion of an image delivered from themain display area of the at least one image modulator near theperipheral compensating area.
 14. A display device according to claim12, wherein said at least one image modulating means comprises aplurality of liquid crystal display panels, and the array ofconvergently transmissive elements and the fresnel lens are arranged forevery liquid crystal display panel.
 15. A display device according toclaim 14, wherein four sets of the liquid crystal display panels, thearrays of convergently transmissive elements and the fresnel lenses arearranged, with each set arranged in respective quarter portions in arectangular region, the screen having a total display area four timesgreater than a display area necessary to receive an image from one setof the liquid crystal display panel, the array of convergentlytransmissive elements and the fresnel lens.
 16. A display deviceaccording to claim 15, wherein a partition is arranged on or near thescreen between two adjacent sets of the liquid crystal display panels,the arrays of convergently transmissive elements, and the fresnellenses, for preventing light from straying from one set into theadjacent set.
 17. A display device according to claim 14, whereinbetween two adjacent liquid crystal display panels, said peripheralcompensating area of one liquid crystal display panel is controlled toprovide an image which is generally identical to a portion of an imagedelivered from the main display area of the adjacent liquid crystaldisplay panel near the peripheral compensating area of said one liquidcrystal display panel.
 18. A display device comprising:at least oneimage modulator; optical lens for magnifying an image output by said atleast one image modulator; a screen for receiving an image from said atleast one image modulator via said optical lens; and the screen has apredetermined display area, and said at least one image modulator has amain display area and a peripheral compensating area arranged such thatthe main display area forms an image on the predetermined display areavia said optical lens and the peripheral compensating area forms animage just outside the predetermined display area via said optical lens.19. A display device according to claim 18, wherein said at least oneimage modulator comprises a plurality of liquid crystal display panels,and the array of convergently transmissive elements and the fresnel lensare arranged for every liquid crystal display panel.
 20. A displaydevice comprising:at least one image modulator; an array of convergentlytransmissive elements receiving light from said at least one imagemodulator for forming an erect and real image; a fresnel lens includinga body having a flat surface and a configured surface with periodicridges, wherein each of the ridges includes a flat crest extendinggenerally parallel to the flat surface and at least one inclined surfaceextending from the flat crest toward the crest of each of the ridges,and the fresnel lens being arranged so that light is made incident fromthe array of convergently transmissive elements to the configuredsurface of the fresnel lens, further wherein the flat crests havevarying widths depending on the positions of the ridges; and a screenreceiving light from said at least one image modulator via the array ofconvergently transmissive elements and the fresnel lens.
 21. A displaydevice according to claim 20, wherein the at least one inclined surfacecomprises a main inclined surface arranged on one side of the flat crestand designed such that light is mainly incident to the body from themain inclined surface, and a minor inclined surface arranged on theother side of the flat crest from the main inclined surface.
 22. Adisplay device according to claim 21, wherein the width of the flatcrest is determined by the following relationship: ##EQU5## where d isthe width of the flat crest, p is the pitch of the ridges, r is theangle of a major light ray made incident to the body from the maininclined surface relative to the axis, θ₁ is the angle of the maininclined surface relative to the flat surface, and θ₂ is the angle ofthe minor inclined surface relative to the axis.
 23. A display devicecomprising:at least one image modulator; an array of convergentlytransmissive elements receiving light from said at least one imagemodulator for forming an erect and real image; a fresnel lens includinga body having a flat surface and a configured surface with periodicridges, the fresnel lens being arranged so that light is made incidentfrom the array of convergently transmissive elements to the configuredsurface of the fresnel lens; and a screen receiving light from said atleast one image modulator via the array of convergently transmissiveelements and the fresnel lens and wherein the screen has a predetermineddisplay area, and said at least one image modulator has a main displayarea and a peripheral compensating area arranged such that the maindisplay area forms an image on the predetermined display area via thearray of convergently transmissive elements and the fresnel lens and theperipheral compensating area forms an image just outside thepredetermined display area via the array of convergently transmissiveelements and the fresnel lens.
 24. A display device according to claim23, wherein said peripheral compensating area of said at least one imagemodulator is controlled to provide an image which is generally identicalto a portion of an image delivered from the main display area of the atleast one image modulator near the peripheral compensating area.
 25. Adisplay device according to claim 23, wherein said at least one imagemodulator comprises a plurality of liquid crystal display panels, andthe array of convergently transmissive elements and the fresnel lens arearranged for every liquid crystal display panel.
 26. A display deviceaccording to claim 25, wherein between two adjacent liquid crystaldisplay panels, said peripheral compensating area of one liquid crystaldisplay panel is controlled to provide an image which is generallyidentical to a portion of an image delivered form the main display areaof the adjacent liquid crystal display panel near the peripheralcompensating area of said one liquid crystal display panel.
 27. Adisplay device according to claim 25, wherein four sets of the liquidcrystal display panels, the arrays of convergently transmissive elementsand the fresnel lenses are arranged, with each set arranged inrespective quarter portions in a rectangular region, the screen having atotal display area four times greater than a display area necessary toreceive an image from one set of the liquid crystal display panel, thearray of convergently transmissive elements and the fresnel lens.
 28. Adisplay device according to claim 27, wherein a partition is arranged onor near the screen between two adjacent sets of the liquid crystaldisplay panels, the arrays of convergently transmissive elements, andthe fresnel lenses, whereby the partition prevents light from strayingfrom one set into an adjacent set.
 29. A display device according toclaim 4, wherein said erect and real image is of substantially identicalsize to an image received from said at least one image modulator.
 30. Adisplay device according to claim 4, wherein said fresnel lens isconfigured for allowing light to divergently travel therefrom.